A control moment gyro (“CMG”) used for roll attenuation in boats is dependent on a heavy flywheel operating at high rotational speeds. The spinning flywheel is supported by bearings that are subjected to high axial and radial loads. As a result, these bearings produce a substantial amount of friction-generated heat, which must be dissipated in order to avoid dangerous heat build up. If the flywheel is supported in a conventional, ambient environment, the heat can be dissipated by air convection, which can be assisted by having a fan blow air across the outer and inner bearing races and the adjacent metal members. But if the flywheel is enclosed in a partial vacuum, e.g., as described in our patent, U.S. Pat. No. 6,973,847, there may not be enough air to permit convection. The same cooling problem may exist in other devices in which flywheels spin in partially evacuated enclosures (e.g., mechanical energy storage devices) and manufacturing processes that use evacuated chambers containing spinning elements that require heat generating bearings. At present, flywheel energy storage devices typically use expensive magnetic bearings (which do not generate frictional heat) instead of much less expensive rolling element bearings. One reason is that there are no proven methods of removing the heat from the inner races of rolling element bearings in a partial vacuum except by jetting or circulating cooling oil through the bearings, and this tends to create large power losses.
Two types of heat flow—conduction and convection—need to be distinguished. Heat conduction occurs by molecules bumping into other molecules. Thus, when you place your hand on a warm radiator, the fast moving molecules in the warm metal bump into molecules in your skin, transferring energy to them. Heat convection occurs when molecules are moved as a consequence of air (or other gas or liquid) flowing from one location to another. Thus, the warm radiator heats a room by conduction of heat to air immediately adjacent the surface of the radiator, and then by convection as that warmed air flows around the room. The warmth in the air is transferred to the occupants of the room by conduction, when the molecules in warm air contact the skin or clothing of the person. Heat conduction may occur through a gas, liquid, or solid. When it occurs through a gas, it can be called gaseous conduction. When it occurs through a solid (e.g., through a metal or other good conductor of heat), it can be called solid conduction.
Fourier's law of heat conduction defines one dimensional heat transfer between two parallel surfaces by gaseous conduction:Q=KA ΔT/ΔXWhere Q=heat transfer (watts)
K=thermal conductivity of the gas (watts/m−Deg C.)
A=area of the parallel surface (m2)
ΔT=temperature differential between the two heat transfer surfaces (deg C.)
ΔX=distance between the heat transfer surfaces (m)
As shown in the equation, the amount of heat transferred is directly proportional to the thermal conductivity of the gas, the area of the surfaces, and the temperature difference between the surfaces, and is inversely proportional to the distance between the surfaces. The thermal conductivity of the gas (K) is constant irrespective of pressure until the pressure is so low that the gas molecular mean free path is equal to or greater than the distance between the surfaces (ΔX). This means that the amount of heat transferred will be independent of pressure until the gas mean free path is equal to or greater than the distance between the surfaces. Below the pressure where the gas molecular mean free path is greater than the distance between the surfaces, the gas molecules will continue to conduct heat but now there is a reduction in the thermal conductivity (and the amount heat transferred) with further reductions in the gas pressure.